Thin films of amorphous germanium-tin alloy (a-Ge1-xSnx) have been prepared by sputtering germanium and tin targets with argon in a radio-frequency magnetron sputtering system. X-ray diffraction reveals that the film for x < 0.38 is amorphous but that crystalline beta-Sn is formed in the amorphous film for x greater than or equal to 0.38. The optical energy gap is expressed by Eg = 0.68 - 0.85x [eV] for x < 0.38. The equation also correlates the pseudo-optical energy gap for the GeSn-beta-Sn composite film.